Weight painting "mozzarella effect"
There are many approaches to solve this kind of problems.
Some of them:

In edit mode select the vertices you need and &quot;assign&quot; weight instead of painting.


In edit mode press P and separate some parts into a new object, weight paint the new object, then rejoin (Ctrl J): the weights will remain intact.

In weight paint mode use Alt B to isolate the zone you want to paint and change the tools behaviour, unclicking the &quot;front faces only&quot; button and selecting the &quot;projected&quot; falloff shape, so that every vertex under the cursor (in a 2D fashion) will get painted.